With many electrons the pattern builds up quicker, but other than that it's not different than a single electron. The electrons in the beam for the most part do not interact with each other and so they can be described by independent wavefunctions. In other circumstances (like the two-electrons-in-a-box problem) there is an interaction and therefore only a single wavefunction for the system.
"Real waves" can interfere with other waves. Wavefunctions are not like that, they can only interfere with themselves.
I'm not arguing at all that something wave-like is happening, I just refuse to identify "electron" with "wave," a la Feynman. This isn't a settled issue!